Question

about 56% of all students have a laptop. randomly sample of 40 students,

probability

1. exactly 16 have a laptop?

2. at least 18 have a laptop?

3. fewer than 18 have laptop?

Answer 1

Let the random variable X denotes the number of students who owns a laptop.

The number of students (n) is 40.

The probability of success (p) that is proportion of students who owns a laptop is 56%, that is, 0.56.

Since, each student is independent of the other and probability of success is same for each student. Hence, assume,

Since n is large enough, the binomial distribution here can be approximated by the normal distribution:

The standardized value of X is:

1)

The probability that out of sample of students, exactly 16 have a laptop is obtained as:

The z-value is obtained using statistical tables.

Therefore, the probability that out of sample of students, exactly 16 have a laptop is 0.0161.

2)

The probability that out of sample of students, at least 18 have a laptop is obtained as:

The z-value is obtained using statistical tables.

Therefore, the probability that out of sample of students, at least 18 have a laptop is 0.9407.

3)

The probability that out of sample of students, fewer than 18 have a laptop is obtained as:

The z-value is obtained using statistical tables.

Therefore, the probability that out of sample of students, fewer than 18 have a laptop is 0.0593.